Documentation for RPNM Series Calculators

Documentation for RPNM Series Calculators                     March 19, 1992


The RPNM series of Calculators is a group of calculator programs
that were produced by Harry Smith of Saratoga CA. These calculators
are unusual in that they not only provide very extended precision
arithmetic (numbers with several thousand digits), but they also
permit the user to define the precision for the calculator (up to
the limit of your particular system's memory). The ability to set
the calculator's precision is desirable to control the speed of the
calculations.

The calculators also utilize Reverse Polish Notation (RPN), thus
the name of the series is RPNMx, for RPN Multiple precision; and x
is used to distinguish between the different individual calculators
of the series. There are currently three different calculators in
the RPNMx series:

      RPNMI - Integer
      RPNMF - Floating point
      RPNMS - Scientific

The Scientific calculator (RPNMS) is the most general, however the
primary reason for different versions, is to permit more digits of
precision when fewer features are required for control or arithme-
tic functions. For example, the Scientific calculator can perform
integer calculations but is limited to about 1/3 as many digits as
the Integer calculator (RPNMI). On the other hand, the Scientific
calculator can produce the transcendental functions normally
required for mathematical calculations; e.g., sin, cos, log, ln, e
to the x power, or x to the y power, etc.; and of course it
operates in floating point.

All of the calculators have the following basic features:

*     RPN arithmetic utilizing a four register stack
      (Plus secondary storage for 2 more registers)

*     Some programmability called "The Learned Line"
      (Admittedly limited but quite useful)

*     Random number generator

*     Radix control to permit numeric bases other than decimal

*     Extensive Operator Control features to enhance effective and
      time efficient utilization:

      *     Display control - permit suppression of intermediate
            results when not needed
            (Note: Recall that a register may have thousands of
            digits to display!)

      *     Separators to group display digits arbitrarily
            e.g., 12,345,678 instead of 12345678 for maybe 4000
            digits. or 123,4567,89AB,CDEF when using the Hexadecimal
            base

      *     Control of display prompts and/or bells

*     Disk I/O capability to permit the calculator to be operated by
      scripts or for off-line control. This is very useful for two
      reasons in particular:

      (1)   Scripts (or files of operations) allows an operator
            sequence to be repeated exactly; thus, a sequence can be
            developed, changed, compared, and saved in as many
            variations as desired.

      (2)   Since the time of some calculations may be quite long,
            the system can be controlled while the user is away (say
            overnight or at work).

*     Other features peculiar to the floating point or scientific
      calculator
      e.g., although the floating point calculator has less preci-
      sion it can operate on numbers as large as 10 to the 39
      thousandth power!

The dynamic range of floating point is extraordinary and is worth
a special note. Consider the dynamic range of the IBM 370 double
precision values. It is about 10 to + or - 75'th power; which is
about the same as other major main frame computers. So how big is
10 to 39,000'th power?

Well, for example: The distance to other stars is usually thought
to be so large that we use light years (LY) rather than miles to
say how far they are. The distance to the nearest star is about 4
LY; 4 is a small number but that is why we used ly in the first
place, because each LY is about 6,000,000,000,000 miles, which is
a big number. On the other hand, the distance across an atom is
such a small length (approximately 0.000000004 inches) that we use
it to measure small distances (this length is called an angstrom).

Now back to the stars. If the distance to a star is large, the
distance to galaxies is much larger. Our nearest galactic neighbor
is about 750,000 LY; and the far ones are so far that they are
measured with megaparsecs (Mpc), which are approximately 3,260,000
LY each. A far galaxy may be more than 3000 Mpc away.

Therefore, it seems fair to say that the distance to a far galaxy
by almost any measure would be a big number; but how far is a far
galaxy in angstrom units? Well, 3000 Mpc, times 3,260,000 LY per
Mpc, times 6,000,000,000,000 miles per LY, times 63,000 inches per
mile, times 254,000,000 angstroms per inch is 10 to the 36'th
angstroms to a far galaxy (approximately).

Another example of a large number might be the number of atoms in
the universe. This has been estimated by some people to be 10 to
the 72'nd power.

So the dynamic range of this calculator can handle "big" numbers
(10 to the 39,000'th power) as well as "small" numbers (10 to the
-39,000'th power).

Can you think of an example of a value of something in the real
world that is "big" or "small"? 

*     The square of the distance to a far galaxy is approximately
      10^36 * 10^36 = 10^72

*     The volume of the known universe in cubic angstroms units is
      4/3 Pi * (10^36)^3 = 10^109 approximately


                                   Wayne Fuqua